Ultracold fermions simulate spin–orbit coupling

Two independent groups of physicists are the first to use ultracold fermionic atoms to simulate "spin–orbit coupling" – an interaction that plays an important role in the electronic properties of solid materials. Both experiments were done by firing laser beams at the atoms, which caused their momentum to change by an amount that depends on their intrinsic spin. Because the interactions between atoms in such simulations can be adjusted with great precision, the breakthrough could shed further light on a range of physical phenomena, including magnetism, topological insulators and Majorana fermions.

Spin–orbit coupling describes the interaction between the intrinsic spin of an electron in a material and the magnetic field induced by the electron's movement relative to its surrounding ions. As well as playing a key role in the magnetic properties of materials, spin–orbit coupling also influences the performance of "spintronic" devices – those that exploit the spin, rather than the charge, of electrons and that could one day lead to faster and more energy-efficient computers.

Quantum simulators

Because of its fundamental nature, physicists are therefore very keen to use clouds of ultracold atoms to simulate spin–orbit coupling. Such "quantum simulations" are carried out by subjecting the gas to laser light and magnetic fields, which lets researchers create interactions between atoms that are similar to those experienced by electrons in a solid. The advantage of these simulations is that – unlike in a solid – the strength of these interactions can be easily adjusted, allowing physicists to test theories of condensed-matter physics.

In 2011 Ian Spielman and colleagues at the National Institute of Standards and Technology (NIST) in Maryland were the first to simulate spin–orbit coupling in an ultracold gas of bosonic atoms. Now, two independent groups – one in China led by Hui Zhai of Tsinghua University and Jing Zhang of Shanxi University, and the other in the US headed by Martin Zwierlein and Lawrence Cheuk at the Massachusetts Institute of Technology (MIT) – have extended Spielman's technique to fermions. As electrons are fermions and not bosons, the new work is much more relevant to electron physics.

Using potassium-40...

The Chinese team began with about two million potassium-40 atoms that are held in an optical trap and cooled to well below the ensemble's Fermi temperature. This means that nearly all the atoms in the gas are in the lowest possible energy state, like the conduction electrons in a metal. The team focused on two closely spaced magnetic energy states, which are used to simulate the spin of the electron – one state corresponding to spin up and the other to spin down.

The team then fired two laser beams into the gas from opposing directions. The laser light is set to resonate with a transition between the two spin states – a process that involves the atoms continuously absorbing and emitting photons. As these photons carry momentum, if an atom absorbs a photon moving in one direction and then re-emits it in the same direction, the atom's momentum will not change. However, an atom can also be stimulated by the opposing beam to emit the photon in the opposite direction – thus changing the atom's momentum. Such an interaction involves a change in the direction of the atom's spin and is therefore analogous to spin–orbit coupling – albeit in 1D.

The Chinese team used its system to study several aspects of spin–orbit coupling. In one experiment, the researchers began with a state in which all the spins are initially pointing in the same direction. They then turned on the spin–orbit interaction by pulsing the lasers for a very short time – just a few hundred microseconds. They found that the spins began to point in different directions in a process known as "dephasing". This is expected from fermions because atoms with the same spin cannot have the same momentum and therefore each atom will be affected differently by the spin–orbit interaction.

Understanding dephasing is important because it has a detrimental effect on technological applications of spin such as spintronics and quantum computing. The team also looked at several other effects related to spin–orbit coupling, including its effect on the momentum distribution of the atoms.

...and lithium-6

The MIT physicists, meanwhile, used a gas of lithium-6 atoms, which meant that their realization of spin–orbit coupling was more difficult than for the Chinese team. The problem is that lighter atoms such as lithium are more prone to heating via the resonant absorption of light. So to get round this problem, the MIT team kept most of its atoms in "reservoir states" in which they do not interact with the light and stayed cool – using radio waves to drive a small number of atoms into the spin–orbit coupling states.

The MIT team focused on showing that ultracold atoms can be used to simulate a "spin diode" – a device that is likely to play a key role in the development of spintronic circuits. It allows spin-up atoms to flow forwards but not backwards, and spin-down atoms backwards but not forward. "The gas acts as a quantum diode, a device that regulates the flow of spin currents," says Cheuk.

Simulating band structure

By applying radio-frequency radiation to the gas, the MIT physicists were also able to simulate a periodic potential similar to that found in a 1D lattice. As expected for real materials, the periodic potential led to the existence of spin-dependent energy bands. According to the team, the ability to create spin-dependent band structures in this way could lead to the simulation of topological insulators.

The spin–orbit coupling simulated by both teams occurs only in 1D and therefore cannot be used to simulate the 2D and 3D systems found in most real-life electronic devices. However, there are several interesting scenarios that can be investigated in a 1D system. For example, it could be used to simulate the behaviour of electrons in semiconductor/superconductor nanowires. Such systems are believed to harbour quasiparticles that resemble Majorana fermions – long sought-after particles that are also their own antiparticle.

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Remarkable work

The spin-orbit(SO) coupling for a particle is represented by the term (kL.S), where S is the spin of the particle that couples to the angular momentum L of its orbit and the parameter k represents its strenght. This SO plays a decisive role in physics such as the basic atomic and nuclear shell models to reproduce correctly the level structures of the systems. Moreover, this SO-coupling also plays a basic role in many other branches of physics such as condensed matter.The origin of this force is that the particle moves in the electric field of its environment, that creats a magnetic field which is proprtional to L and it couples to the spin of the paricle via its magnetic moment. In the present work, the partcles are the ultra-cold Potassium-40 atoms trapped in an optical trap. A resonant laser beam is used via carefully chosen two levels that represent spin up and spin down electrons, to give momentum to the atom that leads to the simulation of spin-orbitcoupling in 1D, because of the nature of the electric field present. The team undertakes a remarkably thorough investigation to prove the presence of SO coupling.